Question

Express ${\left[{\left(\frac{7}{3}\right)}^2\right]}^5$ with a single exponent.

Answer 1

As we know that for any non-zero integer $\text{'}a\text{'}$ and natural numbers $m$ and $n$, we have,

${\left(a^m\right)}^n=a^{mn}$.

So, on applying, we get ,${\left[{\left(\frac{7}{3}\right)}^2\right]}^5$$={\left(\frac{7}{3}\right)}^{2\times 5}={\left(\frac{7}{3}\right)}^{10}$

Hence, ${\left[{\left(\frac{7}{3}\right)}^2\right]}^5$ as a single exponent will be equal to ${\left(\frac{7}{3}\right)}^{10}$.